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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 17 Dec 2012 06:43:16 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/17/t1355744731prhf3jc8d1fd2ce.htm/, Retrieved Wed, 24 Apr 2024 16:46:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200769, Retrieved Wed, 24 Apr 2024 16:46:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact132
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10] [2012-12-17 11:43:16] [d8949b7c39db4d188773a58b86b4d1f1] [Current]
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Dataseries X:
99,42
99,42
99,42
99,42
99,42
109,26
110
110
109,26
100,07
100,07
100,05
100,05
100,05
100,05
100,05
100,05
108,77
111,32
111,6
108,52
103,13
102,87
102,75
102,75
102,75
102,75
102,75
102,75
115,22
115,53
115,4
111,99
107,93
107,43
106,98
106,98
106,98
106,98
106,98
106,98
113,71
118,77
118,54
116,16
110,52
110,06
109,9
109,9
110,72
110,09
110,07
112,45
113,06
119,83
119,84
113,73
110,5
110,12
109,86
110,36
110,36
110,59
112,52
112,1
115,9
122,96
121,26
114,55
111,57
110,65
109,77




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200769&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200769&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200769&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.408032483432256
beta0
gamma0.881226574770473

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.408032483432256 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.881226574770473 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200769&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.408032483432256[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.881226574770473[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200769&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200769&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.408032483432256
beta0
gamma0.881226574770473







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13100.0599.85599358974360.194006410256435
14100.0599.88898900595680.161010994043224
15100.0599.9943545538840.0556454461160456
16100.0599.99589420228890.0541057977111308
17100.0599.84930562413150.200694375868466
18108.77108.4975299475630.27247005243747
19111.32110.8921244118870.427875588112599
20111.6111.0897127162060.510287283793815
21108.52110.580927669378-2.06092766937763
22103.13100.5730033997682.55699660023161
23102.87101.639342238191.23065776181012
24102.75102.1911584131640.558841586835712
25102.75102.561306666170.188693333829633
26102.75102.574921868050.175078131949732
27102.75102.6310625361370.118937463863205
28102.75102.6576242145760.0923757854240392
29102.75102.6031200667820.146879933217676
30115.22111.2668286700363.95317132996375
31115.53115.2443372817170.28566271828322
32115.4115.4268887953-0.0268887952997972
33111.99113.357624876445-1.36762487644479
34107.93106.0415655292071.88843447079267
35107.43106.1432146897361.28678531026362
36106.98106.3674747766960.612525223304445
37106.98106.5664370823260.413562917674057
38106.98106.664703906680.315296093319716
39106.98106.7487718568110.231228143188929
40106.98106.8072956810450.172704318954516
41106.98106.8140006821380.165999317862045
42113.71117.471091096334-3.76109109633356
43118.77116.3877466530922.38225334690782
44118.54117.2627304042291.27726959577124
45116.16115.0262004308361.13379956916407
46110.52110.4293513139840.090648686016408
47110.06109.4835906749010.576409325099291
48109.9109.066261448430.833738551570335
49109.9109.2516957974190.6483042025815
50110.72109.3944830646041.32551693539581
51110.09109.8468992564580.243100743541547
52110.07109.8797380950490.190261904950688
53112.45109.8901094474052.55989055259546
54113.06119.475389051941-6.41538905194076
55119.83120.51372656901-0.683726569009735
56119.84119.5612678520070.27873214799277
57113.73116.842459947588-3.11245994758805
58110.5109.9688315256890.531168474310547
59110.12109.4562179538080.663782046191827
60109.86109.2087773584680.651222641532016
61110.36109.2230060672121.13699393278777
62110.36109.9184677245510.441532275449362
63110.59109.4455389281111.1444610718886
64112.52109.8185982831332.7014017168671
65112.1112.0897308220370.0102691779629396
66115.9115.952660102136-0.0526601021363007
67122.96122.5771624758140.3828375241863
68121.26122.5619703694-1.30197036939995
69114.55117.429143676901-2.87914367690134
70111.57112.55144199136-0.981441991359532
71110.65111.490813080007-0.840813080007266
72109.77110.62289709104-0.85289709103975

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 100.05 & 99.8559935897436 & 0.194006410256435 \tabularnewline
14 & 100.05 & 99.8889890059568 & 0.161010994043224 \tabularnewline
15 & 100.05 & 99.994354553884 & 0.0556454461160456 \tabularnewline
16 & 100.05 & 99.9958942022889 & 0.0541057977111308 \tabularnewline
17 & 100.05 & 99.8493056241315 & 0.200694375868466 \tabularnewline
18 & 108.77 & 108.497529947563 & 0.27247005243747 \tabularnewline
19 & 111.32 & 110.892124411887 & 0.427875588112599 \tabularnewline
20 & 111.6 & 111.089712716206 & 0.510287283793815 \tabularnewline
21 & 108.52 & 110.580927669378 & -2.06092766937763 \tabularnewline
22 & 103.13 & 100.573003399768 & 2.55699660023161 \tabularnewline
23 & 102.87 & 101.63934223819 & 1.23065776181012 \tabularnewline
24 & 102.75 & 102.191158413164 & 0.558841586835712 \tabularnewline
25 & 102.75 & 102.56130666617 & 0.188693333829633 \tabularnewline
26 & 102.75 & 102.57492186805 & 0.175078131949732 \tabularnewline
27 & 102.75 & 102.631062536137 & 0.118937463863205 \tabularnewline
28 & 102.75 & 102.657624214576 & 0.0923757854240392 \tabularnewline
29 & 102.75 & 102.603120066782 & 0.146879933217676 \tabularnewline
30 & 115.22 & 111.266828670036 & 3.95317132996375 \tabularnewline
31 & 115.53 & 115.244337281717 & 0.28566271828322 \tabularnewline
32 & 115.4 & 115.4268887953 & -0.0268887952997972 \tabularnewline
33 & 111.99 & 113.357624876445 & -1.36762487644479 \tabularnewline
34 & 107.93 & 106.041565529207 & 1.88843447079267 \tabularnewline
35 & 107.43 & 106.143214689736 & 1.28678531026362 \tabularnewline
36 & 106.98 & 106.367474776696 & 0.612525223304445 \tabularnewline
37 & 106.98 & 106.566437082326 & 0.413562917674057 \tabularnewline
38 & 106.98 & 106.66470390668 & 0.315296093319716 \tabularnewline
39 & 106.98 & 106.748771856811 & 0.231228143188929 \tabularnewline
40 & 106.98 & 106.807295681045 & 0.172704318954516 \tabularnewline
41 & 106.98 & 106.814000682138 & 0.165999317862045 \tabularnewline
42 & 113.71 & 117.471091096334 & -3.76109109633356 \tabularnewline
43 & 118.77 & 116.387746653092 & 2.38225334690782 \tabularnewline
44 & 118.54 & 117.262730404229 & 1.27726959577124 \tabularnewline
45 & 116.16 & 115.026200430836 & 1.13379956916407 \tabularnewline
46 & 110.52 & 110.429351313984 & 0.090648686016408 \tabularnewline
47 & 110.06 & 109.483590674901 & 0.576409325099291 \tabularnewline
48 & 109.9 & 109.06626144843 & 0.833738551570335 \tabularnewline
49 & 109.9 & 109.251695797419 & 0.6483042025815 \tabularnewline
50 & 110.72 & 109.394483064604 & 1.32551693539581 \tabularnewline
51 & 110.09 & 109.846899256458 & 0.243100743541547 \tabularnewline
52 & 110.07 & 109.879738095049 & 0.190261904950688 \tabularnewline
53 & 112.45 & 109.890109447405 & 2.55989055259546 \tabularnewline
54 & 113.06 & 119.475389051941 & -6.41538905194076 \tabularnewline
55 & 119.83 & 120.51372656901 & -0.683726569009735 \tabularnewline
56 & 119.84 & 119.561267852007 & 0.27873214799277 \tabularnewline
57 & 113.73 & 116.842459947588 & -3.11245994758805 \tabularnewline
58 & 110.5 & 109.968831525689 & 0.531168474310547 \tabularnewline
59 & 110.12 & 109.456217953808 & 0.663782046191827 \tabularnewline
60 & 109.86 & 109.208777358468 & 0.651222641532016 \tabularnewline
61 & 110.36 & 109.223006067212 & 1.13699393278777 \tabularnewline
62 & 110.36 & 109.918467724551 & 0.441532275449362 \tabularnewline
63 & 110.59 & 109.445538928111 & 1.1444610718886 \tabularnewline
64 & 112.52 & 109.818598283133 & 2.7014017168671 \tabularnewline
65 & 112.1 & 112.089730822037 & 0.0102691779629396 \tabularnewline
66 & 115.9 & 115.952660102136 & -0.0526601021363007 \tabularnewline
67 & 122.96 & 122.577162475814 & 0.3828375241863 \tabularnewline
68 & 121.26 & 122.5619703694 & -1.30197036939995 \tabularnewline
69 & 114.55 & 117.429143676901 & -2.87914367690134 \tabularnewline
70 & 111.57 & 112.55144199136 & -0.981441991359532 \tabularnewline
71 & 110.65 & 111.490813080007 & -0.840813080007266 \tabularnewline
72 & 109.77 & 110.62289709104 & -0.85289709103975 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200769&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]100.05[/C][C]99.8559935897436[/C][C]0.194006410256435[/C][/ROW]
[ROW][C]14[/C][C]100.05[/C][C]99.8889890059568[/C][C]0.161010994043224[/C][/ROW]
[ROW][C]15[/C][C]100.05[/C][C]99.994354553884[/C][C]0.0556454461160456[/C][/ROW]
[ROW][C]16[/C][C]100.05[/C][C]99.9958942022889[/C][C]0.0541057977111308[/C][/ROW]
[ROW][C]17[/C][C]100.05[/C][C]99.8493056241315[/C][C]0.200694375868466[/C][/ROW]
[ROW][C]18[/C][C]108.77[/C][C]108.497529947563[/C][C]0.27247005243747[/C][/ROW]
[ROW][C]19[/C][C]111.32[/C][C]110.892124411887[/C][C]0.427875588112599[/C][/ROW]
[ROW][C]20[/C][C]111.6[/C][C]111.089712716206[/C][C]0.510287283793815[/C][/ROW]
[ROW][C]21[/C][C]108.52[/C][C]110.580927669378[/C][C]-2.06092766937763[/C][/ROW]
[ROW][C]22[/C][C]103.13[/C][C]100.573003399768[/C][C]2.55699660023161[/C][/ROW]
[ROW][C]23[/C][C]102.87[/C][C]101.63934223819[/C][C]1.23065776181012[/C][/ROW]
[ROW][C]24[/C][C]102.75[/C][C]102.191158413164[/C][C]0.558841586835712[/C][/ROW]
[ROW][C]25[/C][C]102.75[/C][C]102.56130666617[/C][C]0.188693333829633[/C][/ROW]
[ROW][C]26[/C][C]102.75[/C][C]102.57492186805[/C][C]0.175078131949732[/C][/ROW]
[ROW][C]27[/C][C]102.75[/C][C]102.631062536137[/C][C]0.118937463863205[/C][/ROW]
[ROW][C]28[/C][C]102.75[/C][C]102.657624214576[/C][C]0.0923757854240392[/C][/ROW]
[ROW][C]29[/C][C]102.75[/C][C]102.603120066782[/C][C]0.146879933217676[/C][/ROW]
[ROW][C]30[/C][C]115.22[/C][C]111.266828670036[/C][C]3.95317132996375[/C][/ROW]
[ROW][C]31[/C][C]115.53[/C][C]115.244337281717[/C][C]0.28566271828322[/C][/ROW]
[ROW][C]32[/C][C]115.4[/C][C]115.4268887953[/C][C]-0.0268887952997972[/C][/ROW]
[ROW][C]33[/C][C]111.99[/C][C]113.357624876445[/C][C]-1.36762487644479[/C][/ROW]
[ROW][C]34[/C][C]107.93[/C][C]106.041565529207[/C][C]1.88843447079267[/C][/ROW]
[ROW][C]35[/C][C]107.43[/C][C]106.143214689736[/C][C]1.28678531026362[/C][/ROW]
[ROW][C]36[/C][C]106.98[/C][C]106.367474776696[/C][C]0.612525223304445[/C][/ROW]
[ROW][C]37[/C][C]106.98[/C][C]106.566437082326[/C][C]0.413562917674057[/C][/ROW]
[ROW][C]38[/C][C]106.98[/C][C]106.66470390668[/C][C]0.315296093319716[/C][/ROW]
[ROW][C]39[/C][C]106.98[/C][C]106.748771856811[/C][C]0.231228143188929[/C][/ROW]
[ROW][C]40[/C][C]106.98[/C][C]106.807295681045[/C][C]0.172704318954516[/C][/ROW]
[ROW][C]41[/C][C]106.98[/C][C]106.814000682138[/C][C]0.165999317862045[/C][/ROW]
[ROW][C]42[/C][C]113.71[/C][C]117.471091096334[/C][C]-3.76109109633356[/C][/ROW]
[ROW][C]43[/C][C]118.77[/C][C]116.387746653092[/C][C]2.38225334690782[/C][/ROW]
[ROW][C]44[/C][C]118.54[/C][C]117.262730404229[/C][C]1.27726959577124[/C][/ROW]
[ROW][C]45[/C][C]116.16[/C][C]115.026200430836[/C][C]1.13379956916407[/C][/ROW]
[ROW][C]46[/C][C]110.52[/C][C]110.429351313984[/C][C]0.090648686016408[/C][/ROW]
[ROW][C]47[/C][C]110.06[/C][C]109.483590674901[/C][C]0.576409325099291[/C][/ROW]
[ROW][C]48[/C][C]109.9[/C][C]109.06626144843[/C][C]0.833738551570335[/C][/ROW]
[ROW][C]49[/C][C]109.9[/C][C]109.251695797419[/C][C]0.6483042025815[/C][/ROW]
[ROW][C]50[/C][C]110.72[/C][C]109.394483064604[/C][C]1.32551693539581[/C][/ROW]
[ROW][C]51[/C][C]110.09[/C][C]109.846899256458[/C][C]0.243100743541547[/C][/ROW]
[ROW][C]52[/C][C]110.07[/C][C]109.879738095049[/C][C]0.190261904950688[/C][/ROW]
[ROW][C]53[/C][C]112.45[/C][C]109.890109447405[/C][C]2.55989055259546[/C][/ROW]
[ROW][C]54[/C][C]113.06[/C][C]119.475389051941[/C][C]-6.41538905194076[/C][/ROW]
[ROW][C]55[/C][C]119.83[/C][C]120.51372656901[/C][C]-0.683726569009735[/C][/ROW]
[ROW][C]56[/C][C]119.84[/C][C]119.561267852007[/C][C]0.27873214799277[/C][/ROW]
[ROW][C]57[/C][C]113.73[/C][C]116.842459947588[/C][C]-3.11245994758805[/C][/ROW]
[ROW][C]58[/C][C]110.5[/C][C]109.968831525689[/C][C]0.531168474310547[/C][/ROW]
[ROW][C]59[/C][C]110.12[/C][C]109.456217953808[/C][C]0.663782046191827[/C][/ROW]
[ROW][C]60[/C][C]109.86[/C][C]109.208777358468[/C][C]0.651222641532016[/C][/ROW]
[ROW][C]61[/C][C]110.36[/C][C]109.223006067212[/C][C]1.13699393278777[/C][/ROW]
[ROW][C]62[/C][C]110.36[/C][C]109.918467724551[/C][C]0.441532275449362[/C][/ROW]
[ROW][C]63[/C][C]110.59[/C][C]109.445538928111[/C][C]1.1444610718886[/C][/ROW]
[ROW][C]64[/C][C]112.52[/C][C]109.818598283133[/C][C]2.7014017168671[/C][/ROW]
[ROW][C]65[/C][C]112.1[/C][C]112.089730822037[/C][C]0.0102691779629396[/C][/ROW]
[ROW][C]66[/C][C]115.9[/C][C]115.952660102136[/C][C]-0.0526601021363007[/C][/ROW]
[ROW][C]67[/C][C]122.96[/C][C]122.577162475814[/C][C]0.3828375241863[/C][/ROW]
[ROW][C]68[/C][C]121.26[/C][C]122.5619703694[/C][C]-1.30197036939995[/C][/ROW]
[ROW][C]69[/C][C]114.55[/C][C]117.429143676901[/C][C]-2.87914367690134[/C][/ROW]
[ROW][C]70[/C][C]111.57[/C][C]112.55144199136[/C][C]-0.981441991359532[/C][/ROW]
[ROW][C]71[/C][C]110.65[/C][C]111.490813080007[/C][C]-0.840813080007266[/C][/ROW]
[ROW][C]72[/C][C]109.77[/C][C]110.62289709104[/C][C]-0.85289709103975[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200769&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200769&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13100.0599.85599358974360.194006410256435
14100.0599.88898900595680.161010994043224
15100.0599.9943545538840.0556454461160456
16100.0599.99589420228890.0541057977111308
17100.0599.84930562413150.200694375868466
18108.77108.4975299475630.27247005243747
19111.32110.8921244118870.427875588112599
20111.6111.0897127162060.510287283793815
21108.52110.580927669378-2.06092766937763
22103.13100.5730033997682.55699660023161
23102.87101.639342238191.23065776181012
24102.75102.1911584131640.558841586835712
25102.75102.561306666170.188693333829633
26102.75102.574921868050.175078131949732
27102.75102.6310625361370.118937463863205
28102.75102.6576242145760.0923757854240392
29102.75102.6031200667820.146879933217676
30115.22111.2668286700363.95317132996375
31115.53115.2443372817170.28566271828322
32115.4115.4268887953-0.0268887952997972
33111.99113.357624876445-1.36762487644479
34107.93106.0415655292071.88843447079267
35107.43106.1432146897361.28678531026362
36106.98106.3674747766960.612525223304445
37106.98106.5664370823260.413562917674057
38106.98106.664703906680.315296093319716
39106.98106.7487718568110.231228143188929
40106.98106.8072956810450.172704318954516
41106.98106.8140006821380.165999317862045
42113.71117.471091096334-3.76109109633356
43118.77116.3877466530922.38225334690782
44118.54117.2627304042291.27726959577124
45116.16115.0262004308361.13379956916407
46110.52110.4293513139840.090648686016408
47110.06109.4835906749010.576409325099291
48109.9109.066261448430.833738551570335
49109.9109.2516957974190.6483042025815
50110.72109.3944830646041.32551693539581
51110.09109.8468992564580.243100743541547
52110.07109.8797380950490.190261904950688
53112.45109.8901094474052.55989055259546
54113.06119.475389051941-6.41538905194076
55119.83120.51372656901-0.683726569009735
56119.84119.5612678520070.27873214799277
57113.73116.842459947588-3.11245994758805
58110.5109.9688315256890.531168474310547
59110.12109.4562179538080.663782046191827
60109.86109.2087773584680.651222641532016
61110.36109.2230060672121.13699393278777
62110.36109.9184677245510.441532275449362
63110.59109.4455389281111.1444610718886
64112.52109.8185982831332.7014017168671
65112.1112.0897308220370.0102691779629396
66115.9115.952660102136-0.0526601021363007
67122.96122.5771624758140.3828375241863
68121.26122.5619703694-1.30197036939995
69114.55117.429143676901-2.87914367690134
70111.57112.55144199136-0.981441991359532
71110.65111.490813080007-0.840813080007266
72109.77110.62289709104-0.85289709103975







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73110.276802330692107.229685637481113.323919023904
74110.145540735606106.854527030237113.436554440975
75109.859140511849106.341098119295113.377182904403
76110.577412348923106.846129279698114.308695418149
77110.342435745294106.409456669635114.275414820952
78114.168347335832110.043523039399118.293171632266
79121.041517347814116.7333824215125.349652274128
80119.991222410113115.507264603642124.475180216583
81114.566897625097109.913755817985119.220039432208
82111.85393041451107.0375438287116.670317000319
83111.267121843545106.292844930178116.241398756911
84110.735981188645105.608673720029115.863288657261

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 110.276802330692 & 107.229685637481 & 113.323919023904 \tabularnewline
74 & 110.145540735606 & 106.854527030237 & 113.436554440975 \tabularnewline
75 & 109.859140511849 & 106.341098119295 & 113.377182904403 \tabularnewline
76 & 110.577412348923 & 106.846129279698 & 114.308695418149 \tabularnewline
77 & 110.342435745294 & 106.409456669635 & 114.275414820952 \tabularnewline
78 & 114.168347335832 & 110.043523039399 & 118.293171632266 \tabularnewline
79 & 121.041517347814 & 116.7333824215 & 125.349652274128 \tabularnewline
80 & 119.991222410113 & 115.507264603642 & 124.475180216583 \tabularnewline
81 & 114.566897625097 & 109.913755817985 & 119.220039432208 \tabularnewline
82 & 111.85393041451 & 107.0375438287 & 116.670317000319 \tabularnewline
83 & 111.267121843545 & 106.292844930178 & 116.241398756911 \tabularnewline
84 & 110.735981188645 & 105.608673720029 & 115.863288657261 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200769&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]110.276802330692[/C][C]107.229685637481[/C][C]113.323919023904[/C][/ROW]
[ROW][C]74[/C][C]110.145540735606[/C][C]106.854527030237[/C][C]113.436554440975[/C][/ROW]
[ROW][C]75[/C][C]109.859140511849[/C][C]106.341098119295[/C][C]113.377182904403[/C][/ROW]
[ROW][C]76[/C][C]110.577412348923[/C][C]106.846129279698[/C][C]114.308695418149[/C][/ROW]
[ROW][C]77[/C][C]110.342435745294[/C][C]106.409456669635[/C][C]114.275414820952[/C][/ROW]
[ROW][C]78[/C][C]114.168347335832[/C][C]110.043523039399[/C][C]118.293171632266[/C][/ROW]
[ROW][C]79[/C][C]121.041517347814[/C][C]116.7333824215[/C][C]125.349652274128[/C][/ROW]
[ROW][C]80[/C][C]119.991222410113[/C][C]115.507264603642[/C][C]124.475180216583[/C][/ROW]
[ROW][C]81[/C][C]114.566897625097[/C][C]109.913755817985[/C][C]119.220039432208[/C][/ROW]
[ROW][C]82[/C][C]111.85393041451[/C][C]107.0375438287[/C][C]116.670317000319[/C][/ROW]
[ROW][C]83[/C][C]111.267121843545[/C][C]106.292844930178[/C][C]116.241398756911[/C][/ROW]
[ROW][C]84[/C][C]110.735981188645[/C][C]105.608673720029[/C][C]115.863288657261[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200769&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200769&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73110.276802330692107.229685637481113.323919023904
74110.145540735606106.854527030237113.436554440975
75109.859140511849106.341098119295113.377182904403
76110.577412348923106.846129279698114.308695418149
77110.342435745294106.409456669635114.275414820952
78114.168347335832110.043523039399118.293171632266
79121.041517347814116.7333824215125.349652274128
80119.991222410113115.507264603642124.475180216583
81114.566897625097109.913755817985119.220039432208
82111.85393041451107.0375438287116.670317000319
83111.267121843545106.292844930178116.241398756911
84110.735981188645105.608673720029115.863288657261



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')